I think what I was missing was parts of the model. I need to read up on Inertia. I passed over the Higgs boson, and the Higgs field for a minute. I now have a loose understanding of that. I think I've got an understanding of space, but the idea of time is still perplexing to me. At this point I have reading to do. Thank you Seattle.

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It can be argued that the model of mass curving spacetime is "just" a mathematical device, but it is one that reproduces what we observe.

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I shouldn't say, 'until it doesn't.' I have reading to do, because as yet I don't understand not the mathematics, but the things they reflect. My understanding of time, for example, is severely lacking. I though I understood time, but not. So I have reading to do. Thanks exchemist, for helping to battle ignorance, which in my case is fairly dense, and difficult to quantify mathematically even though it is definitely observable.

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Seems harmless but is it a mathematical model or just a mathsie way of working out how long it will take to get to the next town if you travel at a certain speed? Does the equation just represent 'reality' or is it part of a mathematical model of reality? Turns out it is part of a mathematical model that approximates reality but isn't actually 'real'. In fairness Newton's Universe fits with common experience so we grow up with it as 'reality' and anything else looks like a mathematical model when in fact it's just another mathematical model that is a better approximation to reality when high speeds are involved.

When looking at a map and seeing too points that are 60 miles apart we automatically think [Newton!!] it will take 1 hour to travel between those towns if we travel at 60 miles an hour. Using Newton's (approximate) model we just performed a division - to get a more accurate answer we have to do (slightly) more but the principle of maths->reality and reality->maths remains the same.

Gallileo could have grasped it in the 17th century - you can't tell if a ship is moving - was he saying the laws of physics are independent of motion? Newton virtually had it by the balls - he was that damn clever - but let it go. Einstein was the one that picked up "The laws of physics are the same in every frame" and ran with it.

"The laws of physics are the same in every frame" is what makes Newton's model untenable - what was he thinking?

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Having something in mind does not qualify as something which curves or bends.

You are making spacetime appear as something more than mathematical entity, can you please give a single citation which supports this.

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I see this discussion as fairly pointless.

What would it mean to you for spacetime to be "more than a mathematical entity"? What would that look like, as opposed to spacetime being merely a "mathematical entity"?

When we're talking about "spacetime", in the end we're referring to a scientific theory, just like when we talk about "gravity" or "electricity" or "photons of light". That is, those terms mean something specific when scientists use them.

On the other hand, non-scientists also use them, but generally is a more vague sense. They know that if they plug their toaster into the power point then it provides "electricity", but they don't necessarily know exactly what "electricity" is. In the same way, when most people talk about space and time, or "spacetime", they have a vague idea that space is what they move around in and time is what their watch says, but they don't necessarily have the kind of rigorous understanding that physicists have about those concepts.

So, if you ask me whether "spacetime" is "something more than a mathematical entity", then the answer seems obvious: there must be more to it than "just" maths, because most ordinary (non-scientist) people have something in mind other than maths when they talk about space and time. It is obvious to me, and therefore to try to debate the point is an obvious waste of time.

On the other hand, you seem very fixated on the issue of whether spacetime "really curves", like general relativity says it does. Non-scientist people may have some vague idea about spacetime curving, but they probably understand that less than they understand "electricity". Physicists, on the other hand, can put a mathematical scaffold around the term "spacetime curvature", so that it means something precise.

Spacetime curvature, as in general relativity, is a scientific model. Its aim is to allow us to make useful predictions about what we will observe in the world when we make certain measurements or observations. The success or failure of the concept of "spacetime curvature" then necessarily has to be judged by its predictive success or failure.

Asking whether spacetime really curves is the same as asking whether gravity or electricity "really" exists. Does the theory match our experience? Yes, it does. So, what does that mean? It means we have a good scientific model of something that happens in the real world. And also, it means it can be convenient to talk as if spacetime (whatever that is) actually curves, even though we don't directly perceive that curvature with our senses (arguably).

So, for me it comes back to a shrug and a repeat of my question to you: why does it matter to you if it's "real" or "just a mathematical model"? What is the important difference for you? How do you even tell the difference?

You presumably have something in mind when you talk about "space" or "time", and so does The God, despite his insistence that it's all just maths.

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Fine, we all have something in mind when we talk of space and time. But...

1. Those who do not know SR/GR, they will be totally blank about spacetime.

2. Those who know some physics, but not actual academic SR/GR/metric, they can appreciate that spacetime may be some sort of mathematical co-ordinate system. They will not associate it at par with what they think about space or time as commonly understood.

3. Now comes graduate students of the field : what is important is what is being taught to them about spacetime.

4. Finally the experts :

Now please do not say that we do not know what electricity is, it is not on the same footing as spacetime is.

I have no problem if we talk spacetime as set of worldlines, worldlines would require spatial as well as temporal coordinates. The individual world line or spacetime as a whole of course can be modelled as bending etc in presence of mass/energy. That would make it purely a mathematical entity, devoid of any physical aspect.

The problem comes when it is pushed that 'space' is bending or problem comes when fabric of spacetime like analogies give it a physical attribute.

I will further elaborate, on a straight road if a driver is taking zig zag or curved path, we do not say that road is curvy, but if the road itself is curvy then driver is forced to take that curvy path. So spacetime (in 1-D or 2-D) is a path taken by the object, not that the path background is curvy.

Further when an electron is deflected in presence of other charges, we do not say that background is deflected, we say that particle path is influenced by the presence of other charges.

Problem with spacetime description is that the literature or such discussions give an impression that background is curved; that has no physical meaning. Metric representation is pure maths.

When you drop something it accelerates towards the Earth. Newton calls this "Gravitational Force" which is fine for all ordinary calculations. Einstein claimed this effect was the result of non-uniformity in spacetime. Newton requires that mass somehow creates a field which you can't see whereas Einstein requires that mass somehow distorts spacetime. If Einstein was right as all experimental evidence suggests he is then as you watch an object fall (accelerating) towards the Earth there is no force on on the object - all you are looking at is the effect of spacetime influenced by mass - there is nothing else present to cause the effect.

That's confusing language and gives a kind of impression that spacetime is something physical which is capable of getting distorted.

You are not at fault, this is commonly used language, but necessary. Why necessary? Not very difficult to see, Einstein claimed that gravity is not a force, still the motion was curved, now curved motion will require force that will contradict him, so he curved the road itself and called them straight lines (geodesics) capable of force free motion. Quite clever!

But the problem, if you curve the road, means if spacetime is physical and curved, then the motion of object on a curved surface would require force (high school physics), so he changed the physics, the Euclid geometry also out and now the curves were no longer curves.

Einstein claimed that gravity is not a force, still the motion was curved, now curved motion will require force that will contradict him, so he curved the road itself and called them straight lines (geodesics) capable of force free motion. Quite clever!

But the problem, if you curve the road, means if spacetime is physical and curved, then the motion of object on a curved surface would require force (high school physics), so he changed the physics, the Euclid geometry also out and now the curves were no longer curves.

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Ya know, I have read, on forums like this, some confused and misleading comments regarding differential geometry in general and GR in particular, but this falls into a higher category - namely pure gibberish.

That's confusing language and gives a kind of impression that spacetime is something physical which is capable of getting distorted.

You are not at fault, this is commonly used language, but necessary. Why necessary? Not very difficult to see, Einstein claimed that gravity is not a force, still the motion was curved, now curved motion will require force that will contradict him, so he curved the road itself and called them straight lines (geodesics) capable of force free motion. Quite clever!

But the problem, if you curve the road, means if spacetime is physical and curved, then the motion of object on a curved surface would require force (high school physics), so he changed the physics, the Euclid geometry also out and now the curves were no longer curves.

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But don't forget that by doing this he could account for observations that could not otherwise be explained. That is the reason why we have adopted his model. It fits observed reality better than any alternative yet devised. So he must have been doing something right, eh?

This was my inquery, so: The point of the discussion - to get a grasp of a set of subjects discussed in physics. It was not a pointless question, but maybe you're not talking about the main question, but talking about someone else's reply.

The curving, bending, warping etc of spacetime is something which is on paper, its not that some physical stuff is bending or so.

Now if I tell you, what exactly it is in my opinion, then I will get some points.

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The answer was: Physics doesn't say what things are. It tries to explain observations. Spacetime is a metrical environment to work within as noted by rpenner further on in this discussion. Ignorance is a powerful force here on Earth. That is a hole even physicists want not to fall into. In addition it has history. Mine comes from years of attending to things other than spacetime. BTW, some people are cordial enough to share knowledge with those of us who either forgot aspects of the subject, or never understood it in the first place. Hats off to them.

Indeed. All models all mathematical abstractions. If a given model predicts what we observe, it's a good model.

If it predicts what we see, then what does it mean to say it's "only" a mathematical abstraction? Does space "really" curve? Well that's not really for physics to decide.

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I'm old, and not only are the concepts difficult, but they are complicated to me, because somewhere in the discussion we use real particles with real vectors, and real energies. Who knows, maybe spacetime is constructed of a string matrix. Physics and astrophysics even without the math are subjects filled with amazing things.

The term "spacetime" as associated with general relativity (GR) and its description of gravity is unfortunate, at least within a lay context. The word spacetime and phrase spacetime curvature, in the context of gravitation and GR is not the same as what we think of when we use the words "space" and "time". There may have been a time when Minkowski 4D space, in the context of special relativity could be thought of as the product of our experience of space and time. But within the context of GR and discussions of gravitation things are not as simple.

GR is a geometric description of the dynamic interaction of massive objects, we attribute to gravitation... Simply said, GR describes and predicts what happens, not why. If the why and/or how were known there would be no need to continue a search for quantum gravity and some way to unify GR with quantum mechanics. Thus for a lay audience (and even some not so lay...) understanding what spacetime curvature means in the context of GR, becomes confused with our everyday experience of space and time.

The word Spacetime and phrase Spacetime curvature cannot be easily defined within a lay context and without an at least good understanding of the math. That said space and time as we experience them and Spacetime and Spacetime curvature within the context of GR are all abstract, meaning non physical constructs. That does not mean they do not exist. Just that they are not things we can reach out and touch. They are all three concepts that help us understand and define the world around us.

I hope that both rpenner and James R will forgive my including the following two out of context quotes from long past. I just happened to run across them earlier today when doing a little computer house keeping and this thread when I dropped in to take another look at the greater context of those past discussions. I believe they both say something important, that we all should keep in mind as we discuss physics and especially as we dip our toes into theory...

....
.... Physics isn't about the nature of reality -- Physics is about the behavior of phenomena in reality. Because that's all we can do is poke reality and see how it jumps -- that type of inquiry will never tell you what reality is, only how it behaves. We have very good mathematical models of how it will behave in all sorts of circumstances, but the map is not the territory.

.... Physical models are just that: mathematical models of how a system works. They aim to predict, quantitatively, what will happen in a particular experiment or if you make a particular observation. ....

That's confusing language and gives a kind of impression that spacetime is something physical which is capable of getting distorted.

You are not at fault, this is commonly used language, but necessary. Why necessary? Not very difficult to see, Einstein claimed that gravity is not a force, still the motion was curved, now curved motion will require force that will contradict him, so he curved the road itself and called them straight lines (geodesics) capable of force free motion. Quite clever!

Ya know, I have read, on forums like this, some confused and misleading comments regarding differential geometry in general and GR in particular, but this falls into a higher category - namely pure gibberish.

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Anything but gibberish.
Actually this is an elegant way of presenting something by changing the definitions to avoid internal inconsistencies.

In GR, gravity is not a force but curved motion is there. Newton laws of motion and Euclidean geometry would not have permitted curved motion without force, laws of motion could not have been changed, so redefine the geometry. Thats what is done. But even till today we have to fall back on Newtonian Gravitational Force concept to solve majority of gravity related issues. Give me one example in our day today gravity observation where it is used as curvature of spacetime, not even one, it is invariably force.

Even when we talk of Neutron Star withing GR, we talk of force, pressure and gravitational potential energy.

Even when we talk of orbital motions, we talk of Keplarian Gravitation mechanismnot GR.

Even when we have to design a spacecraft we talk of Newtonian. I do not think that 1969 Apollo moon mission considered GR.

Even when we talk of escape velocity, aka schwarzschild radius issue, we talk of Newtonian.

Even when we talk of BH formation we talk of gravity overcoming all sort of pressures and forces. If gravity is not force as in GR, how could a non force overcome forces?

Precession of mercury can be solved by an additional term in Newtonian, similarly the gravitational lensing. What else? BH?? No its an issue in GR. Spacetime expansion, not so because inflation is not a dispute free concept, we do not know the field required for such inflation.

Let's not mix up the beauty of maths with physics models. Maths of GR could be great but that does not mean..

But don't forget that by doing this he could account for observations that could not otherwise be explained. That is the reason why we have adopted his model. It fits observed reality better than any alternative yet devised. So he must have been doing something right, eh?

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You may be right but there are certain observations which could not be explained by GR. Then?

Pl read any text, since papers will be having complex maths so general articles, on gravitational lensing, one of the first and foremost observation which brought GR in limelight way back 1919 or so.

Now pl enlighten what is spacetime in those GR lensing images/sketches. Visual with some text will help.

It is not sufficient that only Rpenner knows here what is spacetime, many people talk of supporting spacetime without actually knowing what it is.

This was my inquery, so: The point of the discussion - to get a grasp of a set of subjects discussed in physics. It was not a pointless question, but maybe you're not talking about the main question, but talking about someone else's reply.

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Sorry if I gave the wrong impression. I wasn't saying your question was pointless. I was specifically addressing The God's question about whether spacetime is "real" or "just a mathematical device".

Although its clear that you were responding to my post, but both the OP question and my points are quite same.

You gave an indication, or I felt so, that spacetime is more than maths. But you did not clarify how it is anything but maths.

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Here http://math.ucr.edu/home/baez/gr/outline2.html John Baez suggests using coffee grounds to check (theoretically) that what you think spacetime is doing is what it will actually do. By my definition of 'physical' anything that affects coffee is physical.

Here http://math.ucr.edu/home/baez/gr/outline2.html John Baez suggests using coffee grounds to check (theoretically) that what you think spacetime is doing is what it will actually do. By my definition of 'physical' anything that affects coffee is physical.

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Consider a projectile motion, it can be described as..

1. The ball (object thrown) is following its worldlines in some co-ordinate system (x,y,z,t), this world line is parabolic (curved).

2. The ball is following a parabolic (curved path) due to deceleration force in vertical direction (gravity).

3. The ball is moving straight, in a path called geodesic, which is due to curving of spacetime.

4. Your take? If any.

The point is around a magnet the iron fillers will follow some curved path, in electromagnetic field a charged particle follows a curved path, all depending on the initial momentum too. It is the path followed under force. It is not some motion without force.

Can you solve a simple projectile motion in curved spacetime of GR without any reference to force ? Try that.